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set enable_seqscan=off;
CREATE TABLE test_cidr (
	i cidr
);
INSERT INTO test_cidr VALUES
	( '1.2.3.4' ),
	( '1.2.4.4' ),
	( '1.2.5.4' ),
	( '1.2.6.4' ),
	( '1.2.7.4' ),
	( '1.2.8.4' )
;
CREATE INDEX idx_cidr ON test_cidr USING gin (i);
SELECT * FROM test_cidr WHERE i<'1.2.6.4'::cidr ORDER BY i;
     i      
------------
 1.2.3.4/32
 1.2.4.4/32
 1.2.5.4/32
(3 rows)

SELECT * FROM test_cidr WHERE i<='1.2.6.4'::cidr ORDER BY i;
     i      
------------
 1.2.3.4/32
 1.2.4.4/32
 1.2.5.4/32
 1.2.6.4/32
(4 rows)

SELECT * FROM test_cidr WHERE i='1.2.6.4'::cidr ORDER BY i;
     i      
------------
 1.2.6.4/32
(1 row)

SELECT * FROM test_cidr WHERE i>='1.2.6.4'::cidr ORDER BY i;
     i      
------------
 1.2.6.4/32
 1.2.7.4/32
 1.2.8.4/32
(3 rows)

SELECT * FROM test_cidr WHERE i>'1.2.6.4'::cidr ORDER BY i;
     i      
------------
 1.2.7.4/32
 1.2.8.4/32
(2 rows)